High input impedance is required to make all passive basses sound good--it's the preamp part of your amp that buffers the signal before it gets to the power amp. It should be around 1 megohm or so. Keyboards, active basses, etc. are buffered to be low impedance from the outset.
The 0.0047 uF cap will make the treble pickup sound really nasal if you go into a low input impedance. Into a good preamp it actually sounds surprisingly good even soloed. If you run both pickups together with high input impedance the result is that you hear both pickups without any filtering between the two, and it's a totally different sound from the cap bypassed with both pickups on where the treble pickup is putting more bass out but the two pickups filter each other and scoop the sound.